The convergence of such measure-valued jump processes under a mean-field scaling to a large-population limit is shown for example in [1]} via martingale techniques, and in [2]}, where an analytic approach to the convergence of rescaled moment equations is used. In both approaches, the limiting evolution is governed by a non-local evolution equation given by
\(\partial _t u_t(x) =\int _{\mathbb {R}^d} m(y,x)\,u_t(y) \,\mathrm {d}y-u_t(x) \int _{\mathbb {R}^d} c(x,y)\, u_t(y) \, \mathrm {d}y.\) 
